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＜E-Book＞
Field Theory / by Steven Roman
(Graduate Texts in Mathematics. ISSN:21975612 ; 158)

Edition	2nd ed. 2006.
Publisher	(New York, NY : Springer New York : Imprint: Springer)
Year	2006
Language	English
Size	XII, 335 p. 18 illus : online resource
Authors	*Roman, Steven author SpringerLink (Online service)
Subjects	LCSH:Algebra LCSH:Algebraic fields LCSH:Polynomials LCSH:Number theory FREE:Algebra FREE:Field Theory and Polynomials FREE:Number Theory
Notes	Preliminaries -- Preliminaries -- Field Extensions -- Polynomials -- Field Extensions -- Embeddings and Separability -- Algebraic Independence -- Galois Theory -- Galois Theory I: An Historical Perspective -- Galois Theory II: The Theory -- Galois Theory III: The Galois Group of a Polynomial -- A Field Extension as a Vector Space -- Finite Fields I: Basic Properties -- Finite Fields II: Additional Properties -- The Roots of Unity -- Cyclic Extensions -- Solvable Extensions -- The Theory of Binomials -- Binomials -- Families of Binomials This book presents the basic theory of fields, starting more or less from the beginning. It is suitable for a graduate course in field theory, or independent study. The reader is expected to have taken an undergraduate course in abstract algebra, not so much for the material it contains but in order to gain a certain level of mathematical maturity. For this new edition, the author has rewritten the text based on his experiences teaching from the first edition. There are new exercises, a new chapter on Galois theory from an historical perspective, and additional topics sprinkled throughout the text, including a proof of the Fundamental Theorem of Algebra, a discussion of casus irreducibilis, Berlekamp's algorithm for factoring polynomials over Zp and natural and accessory irrationalities. From the reviews of the first edition: The book is written in a clear and explanatory style...the book is recommended for a graduate course in field theory as well as for independent study. - T. Albu, Mathematical Reviews ...[the author] does an excellent job of stressing the key ideas. This book should not only work well as a textbook for a beginning graduate course in field theory, but also for a student who wishes to take a field theory course as independent study. - J.N.Mordeson, Zentralblatt HTTP:URL=https://doi.org/10.1007/0-387-27678-5

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